(vii) 3 000 ml = 3 L (viii) 700 cm < 6·7 m (ix) 300 g = 0·3 kg (x) 5 000 ml < 5·02 L


6. (a) The number 1 is included and the number line is a thick shaded line, which means x ∈ ℝ


7. (i) x > 2, x ∈ ℕ (ii) x > −4, x ∈ ℝ (iii) x ≤ −2, x ∈ ℤ (iv) 0 < x < 2, x ∈ ℕ


8. (i) x = {4, 5, 6, 7, 8} (ii) x = {6, 5, 4, 3, 2} (iii) x = {4, 3, 2, 1, 0} (iv) x = {−5,−4,−3,−2, −1}


Practice questions 32.2


1. (i) x > 8, (ii) x < 5, (iii) y > 7, (iv) b ≤ 3 2. (i) x ≥ 4, (ii) y < 2, (iii) x ≥ −1, (iv) y ≥ 4 3. (i) z ≤ −1, (ii) y ≤ 7, (iii) x < 18, (iv) x ≤ 7, (vi) –7


4. (i) z ≤ 5, (ii) z ≥ 1, (iii) x ≥ 1, (iv) x ≤ 4 5. (i) x > −9, (ii) z > −3, (iii) x ≥ −12, (iv) x > 8


6. x = { 6, 7, 8} 7. (i) 4x + 2 ≤ 30 (ii) x = 7, he can buy 7 books


8. (i) 2y − 9 < 41 (ii) 24


9. (i) 4m + 5 > 60 (ii) Ann = €14, Mary = €28, Angela = €19


Revision questions


32A Core skills 2. (i) x > 7, (ii) x < 4, (iii) b > 2 3. (i) x < 2 ∴ 1 and−1, (ii) −8 < x∴ −6, (iii) x < −8∴ −10 and−9


4. (i) x < 2, (ii) b < 2, (iii) x < 1, (iv) y > 2 5. (i) {−2, −3, −4, −5, −6} (ii) −2 is the largest


6. (i) {2, 1, 0, −1, −2} (ii)


(iii) 2 is the largest 32B Taking it further


1. 9x + 54 > 99 2. 3(y − 7) ≤ 12 3. 4z − 8 ≥ 28 4. Length = 5 m, width = 3 m


5. (i) 500 − 25w ≥ 200 (ii) 12 weeks


6. (i) 2·20 + 0·65k ≤ 10 (ii) 12 km


7. 10 days


Unit 33 Non-linear relationships


Practice questions 33.1 1. (i) Linear, first difference is constant (ii) Linear, first difference is constant (iii) Non-linear, the first difference is not constant


(iv) Non-linear, first difference is not the constant


(v) Non-linear, first difference is not constant


Infinite number of solutions 4. (a)


2. (a)


(i) Non-linear, first difference is not constant


(ii) Linear, first difference is constant


(iii) Non-linear, first difference is not constant


3. (a)


(i) Non-linear, first difference is not constant


(ii) Non-linear, the first difference is not constant


(iii) Linear, first difference is constant


(i) Linear, first difference is constant


(ii) Non-linear – the first difference is not constant


(iii) Non-linear – the first difference is not constant


5. (ii) 5; 8; 11; 14; 17 (iii) Linear, first difference is constant


6. (i) 1; 7; 19; 37; 61 (ii) Non-linear, first difference is not constant


Practice questions 33.2


1. (i) 16; 9; 4; 1; 0; 1; 4 (iii) This is U-shaped graph. It has a positive x2


coefficient


2. (i) 11; 6; 3; 2; 3; 6; 11 (iii) This is U-shaped graph. It has a positive x2


coefficient 3. (i) 12; 6; 2; 0; 0; 2


Practice questions 33.3 1. (i) 5x + 20, (ii) 2x + x2


, (iii) 6y2 2. (i) a2


(iv) yx + y, (v) 12ab − 4a2 + 7a + 12, (ii) 3x2


(iii) y2 3. (i) 2x2 4. (i) x2 5. (i) x2 (v) 16x2


(iii) −3x2 (v) 49x2


(iii) k2 (v) 6x2


+ 3y + 2, (iv) x2 + 2x + 1 + 16x + 4, (vi) 4m2 − x − 10, (ii) 6x2 + 7x − 2, (iv) x2 − 16, (vi) x2


+ 4x − 5, (ii) a2 − 2k − 3, (iv) x2 − 4x − 2, (vi) 2b2 + x − 2, (ii) x2


(iii) 10c2 − c − 2, (iv) x2 (v) 3n + 3, (vi) −4c + 2


Practice questions 33.4 1. (i) x2


(iv) x2


− 16, (ii) x2 − 1


− 4, (iii)m2 − 4,


2. (i) (x − 2), (ii) (x + 15), (iii) (x + 100) 3. (i) (x − 3)(x + 3), (ii) (x − 5)(x + 5), (iii) (n − 12)(n + 12)


4. (i) (x + 1)(x − 1), (ii) (x − 20)(x + 20), (iii) (t − 10)(t + 10)


5. (i) (x + 7)(x − 7), (ii) (x − 13)(x + 13), (iii) (y − 9)(y + 9)


6. 16 − x2 7. 4 − w2 8. (i) (y − 14)(y + 14), (ii) (11 − x)(11 + x), (iii) (6 − p)(6 + p), (iv) (a − b)(a + b), (v) (w − t)(w + t), (vi) (x − y)(x + y)


9. Perimeter = 12 Perimeter = 4x


10.Perimeter = 4a Perimeter = 4b


+ 2x − 3, + 3x − 10, − 6y, , (vi) st − 2s2 + 7x + 2, + 20m + 25


− 13x + 6, − 1,


− 12x + 36 − a − 6,


− 4x + 4, + b − 3


Practice questions 33.5 1. (i) x2


(ii) x2 (iii) m2


2. y2 3. (i)


(ii) 4. (i) (ii)


+ 10x + 24 + 12x + 20 − 8m + 15


+ 19y + 90


(x + 2)(x + 5) (x + 3)(x + 2) (x + 3)(x + 1) (x + 1)(x + 2)


5. (x − 4)(x − 3) 6. (i)


(ii) 7. (i)


(iii) (n + 2)(n + 5) (x − 4)(x − 1)


(x − 6)(x − 2)


(iii) (q − 6)(q − 4) (iv) (x − 12)(x − 1) (x + 4)(x + 2) (x + 9)(x + 5)


(ii)


8. x2 9. (i)


(iii) (x − 11)(x − 1) (iv) (w + 5)(w + 2) + 14x + 40


(ii)


(x + 9)(x + 2) (p − 10)(p − 1)


10.(a + 5)(a + 3) 11.(i)


(ii) 12.(i) (ii)


(iii) (x + 12)(x + 1) (x − 6)(x − 4)


(x + 9)(x + 5)


(iii) (x − 2)(x − 2) (x + 3)(x + 3) (x + 16)(x + 3)


(iii) (x + 9)(x + 3)


13.Length (x + 8), width (x + 4) 14.(x + 4)(x + 4)


Practice questions 33.6 1. (i) x2


(ii) x2 (iii) m2


2. y2 3. (i)


(ii) (ii)


6. x2 7. (i)


− 5x − 14 + 5x − 24 − 2m − 24


− 12y + 32


(x + 9)(x − 2) (x − 3)(x + 4)


4. (x − 6)(x + 2) 5. (i)


(x + 6)(x − 1) (x − 3)(x + 1)


(iii) (m − 4)(m + 3) (iv) (w − 3)(w + 2) − 2x − 24


(ii)


(x + 6)(x − 2) (p − 2)(p + 1)


8. (a − 4)(a + 2) 9. (i)


(ii) 10.(i) (ii)


(iii) (x + 4)(x − 3) (x − 8)(x + 3)


(x − 6)(x + 4)


(iii) (x − 5)(x + 8) (x + 10)(x − 2) (x − 30)(x + 2)


(iii) (x + 2)(x − 1) (iv) (x + 2)(x – 4)


11.(x + 6)(x − 1) 12.(x − 7)(x + 6)


Practice questions 33.7


1. (i) 5a + 6, (ii) 5x − 2, (iii) 3y + 1, (iv) y − 2 2. (i) (x + 3), (ii) (x − 8), (iii) (x − 3) 3. (i) (x + 2), (ii) (x + 4), (iii) (x − 3) 4. x − 3 5. x − 10 6. x + 2 7. x + 2 8. t + 18 9. x + 7 10.x + 20 11.x + 12


Answer key 593


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